To make time-domain computation more efficient in optical structures,
the wave equation is rewritten to track only the envelope of the elect
ric field. The resultant equation is complex in nature and it is solve
d via a mapping concept and a Pade approximation. Compared to the fini
te-difference time-domain algorithm, this method takes two orders of m
agnitude less memory. This method is applied to the propagation of a 5
00 fsec pulse in a waveguide over 2 mm. Transient behavior and the eff
ects of waveguide parameters are demonstrated.